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Recent questions and answers in Engineering Mathematics
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1
GATE2020CE11
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order nonlinear equation a second degree nonlinear equation
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
partialdifferentialequation
engineeringmathematics
0
votes
0
answers
2
GATE2020CE12
The value of $\lim_{x\to\infty}\dfrac{x^25x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
engineeringmathematics
limit
calculus
0
votes
0
answers
3
GATE2020CE13
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
engineeringmathematics
linearalgebra
linearinterpolation
0
votes
0
answers
4
GATE2020CE14
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
engineeringmathematics
0
votes
0
answers
5
GATE2020CE118
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
asked
Feb 28, 2020
in
Probability and Statistics
by
jothee
(
2.7k
points)
gate2020ce1
probabilityandstatistics
engineeringmathematics
probability
numericalanswers
0
votes
0
answers
6
GATE2020CE126
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
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Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce1
ordinarydifferentialequation
engineeringmathematics
0
votes
0
answers
7
GATE2020CE127
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finitedivideddifference scheme (with step length $=h$ ...
asked
Feb 28, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce1
calculus
functions
engineeringmathematics
0
votes
0
answers
8
GATE2020CE139
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______
asked
Feb 28, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce1
calculus
engineeringmathematics
integrals
numericalanswers
0
votes
0
answers
9
GATE2020CE140
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&3 \\ 4&4&6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
asked
Feb 28, 2020
in
Linear Algebra
by
jothee
(
2.7k
points)
gate2020ce1
matrixalgebra
linearalgebra
engineeringmathematics
numericalanswers
0
votes
0
answers
10
GATE2020 CE21
The ordinary differential equation $\dfrac{d^2u}{dx^2}$ 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
ordinarydifferentialequation
engineeringmathematics
0
votes
0
answers
11
GATE2020 CE22
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
engineeringmathematics
differentialequations
0
votes
0
answers
12
GATE2020 CE23
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NONzero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce2
calculus
engineeringmathematics
integrals
0
votes
0
answers
13
GATE2020 CE24
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
partialdifferentialequation
engineeringmathematics
0
votes
0
answers
14
GATE2020 CE218
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
asked
Feb 13, 2020
in
Probability and Statistics
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
probabilityandstatistics
engineeringmathematics
probability
0
votes
0
answers
15
GATE2020 CE224
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{1}$, round off to two decimal places) at $y = 0$, is ________.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
calculus
engineeringmathematics
gradient
0
votes
0
answers
16
GATE2020 CE226
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1xe^\frac{x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{x}{3} + C_2xe^\frac{x}{2}$
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
ordinarydifferentialequation
engineeringmathematics
0
votes
0
answers
17
GATE2020 CE227
A $4 \times 4$ matrix $[P]$ is given below $[P] = \begin{bmatrix}0 &1 &3 &0 \\2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$ The eigen values of $[P]$ are $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
asked
Feb 13, 2020
in
Linear Algebra
by
jothee
(
2.7k
points)
gate2020ce2
matrixalgebra
linearalgebra
engineeringmathematics
0
votes
0
answers
18
GATE2020 CE239
The Fourier series to represent $x x^2$ for $\pi\leq x\leq \pi$ is given by $ xx^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
partialdifferentialequation
engineeringmathematics
0
votes
0
answers
19
GATE2020 CE240
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The absolute error in the computed volume ( in $cm^3$ ,round off to three decimal places), is ________
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020ce2
numericalanswers
engineeringmathematics
+2
votes
1
answer
20
GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=1$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ ... $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
answered
Jan 17, 2020
in
Calculus
by
KUSHAGRA गुप्ता
(
140
points)
gate2019ce1
calculus
limit
engineeringmathematics
0
votes
0
answers
21
GATE2017 CE21
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
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Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017ce2
engineeringmathematics
equations
0
votes
0
answers
22
GATE2017 CE22
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017ce2
engineeringmathematics
partialdifferentialequation
0
votes
0
answers
23
GATE2017 CE219
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
vectorcalculus
divergence
numericalanswers
calculus
engineeringmathematics
0
votes
0
answers
24
GATE2017 CE220
A twofaced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
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Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017ce2
numericalanswers
engineeringmathematics
0
votes
0
answers
25
GATE2017 CE226
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$axis. The coordinates of the tangent point would be $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
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Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
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gate2017ce2
engineeringmathematics
tangentpoint
0
votes
0
answers
26
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
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Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
definite
integral
calculus
engineeringmathematics
0
votes
0
answers
27
GATE2017 CE228
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
asked
Aug 7, 2019
in
Linear Algebra
by
gatecse
(
3.9k
points)
gate2017ce2
matrix
linearalgebra
engineeringmathematics
0
votes
0
answers
28
GATE2017 CE229
Consider the following secondorder differential equation: $y’’ – 4y’+3y =2t 3t^2$. The particular solution of the differential solution equation is $ – 2 2tt^2$ $ – 2tt^2$ $2t3t^2$ $ – 2 2t3 t^2$
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Aug 7, 2019
in
Partial Differential Equation (PDE)
by
gatecse
(
3.9k
points)
gate2017ce2
differentialequation
particularsolution
engineeringmathematics
0
votes
2
answers
29
GATE2019 CE2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
answered
Feb 20, 2019
in
Numerical Methods
by
moinkhan
(
140
points)
gate2019ce2
numericalmethods
numericalanswers
engineeringmathematics
+1
vote
0
answers
30
GATE2019 CE1: 2
Consider a twodimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
asked
Feb 14, 2019
in
Partial Differential Equation (PDE)
by
Arjun
(
2.8k
points)
gate2019ce1
laplaceequation
continuity
partialdifferentialequation
engineeringmathematics
+1
vote
0
answers
31
GATE2019 CE1: 3
A simple massspring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t$, the equation of motion for the free vibration of the system is $m \ddot{z} + kz = 0$. The natural frequency of the system is $\dfrac{k}{m} \\$ $\sqrt{ \dfrac{k}{m}} \\$ $\dfrac{m}{k}\\$ $\sqrt{ \dfrac{m}{k}}$
asked
Feb 14, 2019
in
Engineering Mathematics
by
Arjun
(
2.8k
points)
gate2019ce1
engineeringmathematics
+1
vote
0
answers
32
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) + \dfrac{h^3}{3!}{f}'''(x)+\dots \infty \\$ $f(x)h{f}' (x) + \dfrac{h^2}{2!}{f}''(x)  \dfrac{h^3}{3!}{f}'''(x)+ \dots \infty \\$ ... $f(x)h{f}' (x) + \dfrac{h^2}{2}{f}''(x)  \dfrac{h^3}{3}{f}'''(x)+ \dots \infty $
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
taylorseries
calculus
engineeringmathematics
0
votes
0
answers
33
GATE2019 CE1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is ________
asked
Feb 14, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019ce1
probability
numericalanswers
probabilityandstatistics
engineeringmathematics
0
votes
0
answers
34
GATE2019 CE1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
maximaminima
calculus
engineeringmathematics
0
votes
0
answers
35
GATE2019 CE1: 27
A onedimensional domain is discretized into $N$ subdomains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\Delta t$, the forwardtime and centeredspace finite difference approximation at i th node and n th time step, for the ...
asked
Feb 14, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019ce1
probabilityandstatistics
engineeringmathematics
discreterandomvariables
0
votes
0
answers
36
GATE2019 CE1: 30
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$? $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1} \\$ ... $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi 1}$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
calculus
engineeringmathematics
functions
0
votes
0
answers
37
GATE2019 CE1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
asked
Feb 14, 2019
in
Ordinary Differential Equation (ODE)
by
Arjun
(
2.8k
points)
gate2019ce1
differentialequation
numericalanswers
engineeringmathematics
0
votes
0
answers
38
GATE2019 CE2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & 2 & 6 \end{bmatrix}^T$ is $\sqrt{12}$ $\sqrt{24}$ $\sqrt{48}$ $\sqrt{56}$
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
2.8k
points)
gate2019ce2
matrixalgebra
linearalgebra
engineeringmathematics
0
votes
0
answers
39
GATE2019 CE2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2a^2} \\$ $\dfrac{s}{s^2+a^2}$
asked
Feb 12, 2019
in
Engineering Mathematics
by
Arjun
(
2.8k
points)
gate2019ce2
ordinarydifferentialequation
engineeringmathematics
laplacetransform
0
votes
0
answers
40
GATE2019 CE2: 3
The following inequality is true for all $x$ close to $0$. $2\dfrac{x^2}{3} < \dfrac{x \sin x}{1 \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
asked
Feb 12, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce2
limit
calculus
engineeringmathematics
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